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Q: TION 9 Prove by Induction that for every natural number n, 3"–1 is a multiple of 2? Attach File…

A: We prove by induction

Q: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

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Q: Prove that the hundreds digit of n20 is even.

A: To Prove that the hundreds digit of n20 is even.

Q: Prove dis prove that the or smallest non- commutative ving is of order 4-

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Q: prove th na

A: The equation given is ,  ∇×F¯θ=1rsinθ∂Fr∂ϕ-1r∂r·Fϕ∂r. The curl of the function is given as, curl…

Q: Without using any theorems from the book, prove the following statement: The sum of any two odd…

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Q: Use Euler's Theorem to find a number x between 0 and 28 with x85congruent to 6 modulo 35. (You…

A: Here finds the value of x for which: x85≡6mod35 and x lies between 0​  to 28

Q: Is given in th

A: The most repeating games used by the researchers that can be played quickly. It is discovered that…

Q: The diagram below shows ten circles joined by five lines with three circles Place all the…

A: Requirements: Numbers should range from 1 to 10.   Every line has three circles.   3. The amount for…

Q: Starting with the integer 72021, we remove the leftmost digit and add it to the remaining integer.…

A: Observation 1: After each step, the difference of the numbers before and after is divisible by 9.…

Q: Show that im n /-

A: Limit of the sequence

Q: Show that 3n^ 2+8nlogn is big-Oh (n ^2 )

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Q: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

Q: prove that tan(ix)= itanh(x)

A: Here we prove thattanix=i tan hx

Q: -, first prove that )" 6.

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Q: show that 2 tan 1/3 + tan 1/7 =n/4

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Q: 2. Prove that L(cashkt)= ki 52-K2

A: To prove that  L(cosh(kt))=ss2-k2

Q: Which positive integers less than 20 are relatively prime to 20?

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Q: Every even integer greater than 2 is sum of two primes? Give your views on this?

A: We know that 2 is even prime. And all other primes are odd.

Q: Prove Simple disprove is Bing That Characteristic af Prime or either Zero or

A: A simple ring R is a ring with unit such that the only two-sided ideals are R and (0). The…

Q: show that: (For real nu

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Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

A: Cosets Definition: Let G be a group and let H is a nonempty subset of G. A left coset of H in G is a…

Q: Let a,n be integers with 2 <n and pod loa,n) = %3D Show that if UIzn) - SanZ;tEZ U(Zn) then ak #1…

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Q: Prove 2- = =4 has infinite many Solu thans ZEC.

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Q: 23. Find de V100- tan O coton 2 Opbon 1

A: We have the given integral as ∫dx100-9x2 On solving the given integral furthermore, we get the…

Q: Let n, m, a, b be positive integers. motl Lof oontredietion u th

A: Given, n, m, a, b be positive integers. To prove that…

Q: All Fermat's number is clearly odd numbers

A: Fermat number.

Q: ) that Prnve Seck -1

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Create a proof for the fc

A: Given,           1.        ~R⊃~Q2.        ~R

Q: 2. Show that (i) tan 48° tan 23° tan 42° tan67° =1

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Q: EX Find theno of letter strings of length H that contain the letter y exactly 3-himes and contain…

A: Total number of letters = 26 Letter y can occur only thrice. Letters m,b,t,k can occur only once.…

Q: 1- 9/if it of Prove that yś(-)- TT

A: In the question it is asked to prove y'(0)=π for the given function y=2xcos-1(2x)-1-4x2.

Q: Suppose x is a fixed real number with x 2 -1. For n2 1, prove using mathematical induction: (1+ x)"…

A: Here we will show that given statement is true by mathematical induction method.

Q: Use Chinese theorem to find all positive integers that makes this congruence true:        x = 2 mod…

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Q: Negate the statement: For all positive integers, n, there exists a positive integer, k, so that…

A: The negation of a statement is:- Statement:- p implies q. Negation:- p does not imply q.

Q: sum of two even integers is even

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Q: The sum of any two integers of the from 4k + 1 is always: Even O prime Zero Odd

A: If a number n is not divisible by 2 then it is an odd number.  If a number n divisible by 2 then it…

Q: Find th: units digitof 3" ++ 11* ", whe re e and n: arc: nan-npitve intrgers

A: To solve this question we need to find out unit digit of each term and then add these unit digits to…

Q: Question 1. Show that if seven integers are selected from the first 10 positive integers, there must…

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Q: se Euler's Theorem to find a number x between 0 and 28 with x85 congruent to 6 modulo 35. (You…

A: By using the fernet's theorem: If a and n are co prime. That is (a,n)=1 then aϕ(n)≡1modn For n=35…

Q: : Use he comparism test to prove hat n-2 Converyes

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Q: 5!, called 5_______ , is the product of all positive integers from_________ down through________ .…

A: For any positive integer n, n! is the product of all the positive integers  from 1 to n. That is,…

Q: Find all Hy reer digit numbers with diteterent digite sucu that tyose Hyree digit aumbere au…

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Q: Prove that tim 51

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the first 4 terms of Toaylor Polyuocuial generated by fCx)= xlnx at a=2.

A: We find first four terms of Taylor polynomial generated by f(x)=xln(x) at a=2.

Q: 15 of 20 -722 –8x =? limz→00 3–72²+6x+6 O Does not exist O 00 O 7

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Q: Suppose that n students take a quiz and their scores sum to 150. What is the smallest number n to…

A: Pigeonhole Principle: The pigeonhole principle states that if n items are put into m containers with…

Q: Prove that 1 tan 7 1 + tan tan 13 9.

A: Given : tan-117+tan-1113 = tan-129

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.